1. (a) Compute A−¹ if A = /1 0 1 33 4 223 (b) Use A−¹ to solve Ax = b, if b = (1, 1, 1)ª.

Q: 13.Show that the third-order Adams-Moulton formula is yn+1=yn+h12(5fn+1+8fn−fn−1).

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Q: 1. Solve the following first-order equation: (2.ry +3y?)dr - (2ay+a)dy = 0. %3D

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Q: Exercise(6): (1) Solve the following Cauchy-Euler differential equations: (a) 4r y" +4.ry-y = 0.

A: Solution:

Q: Solve an = an-1 +3n² – 3n+1 with A, = 0

A: We will find the solution of given recurrence equation by rearranging terms on the non homogeneous…

Q: 1. Find 2(3z + 4)² dz.

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Q: If (In x)2 c (a (In x)? + b in x +c) + constant, then 2 a + 28 b + 18 c = 32

A: Solving the above given integral

Q: Solve the equation In (x + 2) + In (x – 1) = In (9x – 17) and check your answers (True / False) %3D

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Q: Solve for A. ЗА t3D A =|

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Q: Solve the First ODE (3y* – x*)dx = 3xy'dy || 4-4ln(2x)+c А-у %3D 4 4-4ln(x)+c B- y = 2 4-4ln(x)+c C-…

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Q: .. Solve the following equation for r. In(a? – 16) + In(x + 4) = In(2x +3) %3D

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Q: Verify that x = C1et + C2 is a solution to x′′ − x′ = 0.

A: To Verify that x = C1et + C2 is a solution to x′′ − x′ = 0.

Q: 4. If ā= 3i - 2j and b=-5i- j, express 3 a -b in terms of i and j.

A: This is a vector problem

Q: Determine the inverse of Ax) = (x+2)² -3. j(x) =-2+x+3 b. (x)=-3±V+2 f(x) =-2+ x+3 d. (x)=-3+ +2 %3D…

A: The function is given by y = fx = x+22-3                                          ..........1 To…

Q: -6 14 (-7 15 , 18. Solve for X, if X³ = (). 0 2 Ans. X = -1 3

A: We are given that for a matrix X, such that X3=-614-715. We need to find the value of X. Let X =…

Q: Solve for A 10. A= 5-2 1 2

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Q: Solve (1- + xp z_(hx [y² + x² (1 1)-2] dy : dy = 0 xy)

A: We have to solve the given differential equation.

Q: Compute the following: (a) Arg((v3+ i)"). (b) The solution to (3 – 4i)z = 11 + 2i write the answer…

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Q: Consider x4 + 4 = 0. Find all solutions of this equation in Z4. Find all solutions of this equation…

A: We have given an equation, x4+4=0. We need to find all solutions of this equation in ℤ4 and ℤi.…

Q: 2 A=[²2 1 4] IF A= 2 and B= 3 2 L3 4 31 1 2] Find AB :

A: Matrix multiplication is always done from each row to each column, i.e., row to column…

Q: Solve for x. 5 12х — 7 - х — 7 x + 4 x2 – 3x — 28 - - - ||

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Q: I. Solve the following to Notation z = x + iy 1. In(-7) 2. z = i Z1 3. For Z, = 8+ 3i ; Z2 = 9 – 2i…

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Q: (1) Solve the following Cauchy-Euler differential equations: (a) 4r y"+4ry - y = 0.

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Q: If a = 2 + i, and b = 3 – 2i, what is a/b?

A: Given a=2+i, b=3-2i we find ab

Q: 2. Let X and Y be continuous random variables having the joint density function: [c(x² + y²) 0 f(x,…

A: Given that        c = 3/2  The the joint pdf of x and y is given in the question.

Q: Show that the equation x³ - 3x + 1 = 0 has exactly · 3x + 1 = 0 has exactly one solution in [−1, 1].

A: First we show that given equation has atleast one solution in [-1,1]. Then, by method of…

Q: (a) Find a and b such that −3ai − (−1− i )b = 3a−2bi

A: The answer is in step 2.

Q: Find the solutions to x³ - ex² - 1 = 0 to second order in €.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Write down three equations for c, d, e so that cu+ dv + ew = b. Can you somehow find c, d, e for…

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